Supernova Remnant (def.): The expanding glowing remains from a supernova.
Neutron Star (def.): A dense ball of neutrons that remains after a supernova has destroyed the rest of the star. Typically neutron stars are about 20km across, and contain more mass than the Sun.
Field Guide to Supernovas, Supernova Remnants & Neutron StarsChandra Images: Supernovas & Supernova Remnants